On the central limit theorem for modulus trimmed sums

Alina Bazarova, István Berkes and Lajos Horvath

Statistics & Probability Letters, 2014, vol. 86, issue C, 61-67

Abstract: We prove a functional central limit theorem for modulus trimmed i.i.d. variables in the domain of attraction of a nonnormal stable law. In contrast to the corresponding result under ordinary trimming, our CLT contains a random centering factor which is inevitable in the nonsymmetric case. The proof is based on the weak convergence of a two-parameter process where one of the parameters is time and the second one is the fraction of truncation.

Keywords: Modulus trimming; Stable distribution; Iid sums; Central limit theorem (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1016/j.spl.2013.12.006

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